This page will
show you how you can work out the mathematics of a planet's productivity

Let's see how the sun's energy flows in the Biosphere.

Warning: I am making a lot of assumptions and doing
a lot of rounding in the math here. My numbers may be off by
several thousand percent, but I think the process is all right.

Try to understand the basic idea, and don't use my math
numbers
on any Important Exams unless you have checked them out!

Dr Viau says, "Gerald Nordley and Mark Wistey
were kind enough to help with this, but I made the mistakes all
by myself!"

The Solar Constant

How much of the sun's energy gets to the surface of
the earth?

The earth gets only 2 billionths of the sun's energy, but
that is still a lot. However, you can see on the chart that life
(through photosynthesis) uses only .023% of the energy
that reaches the surface of the earth.

34% of the sun's energy is reflected back into space by snow
and clouds. This reflective quality of a planet is called its
albedo.

42% of the energy goes to warm the land and water. The warmth
of the earth is constantly being radiated into space, and the
sun's energy replenishes this warmth.

The water cycle -- evaporation and precipitation -- uses 23%
of the solar energy.

Winds and ocean currents use 1%.

The amount of energy that gets to the earth's surface
at the equator at noon is called

The Solar Constant.

Let's think about this on a small scale that will
make sense to us.

Let's think about how many of the KiloCalories that
we use to measure food fall onto an area that is one meter square.

(A meter is pretty close
to a yard in length, so a square yard and a square meter are roughly the same size.)

At the Equator:

We find how many KiloCalories
falls onto one square meter each day

This turns out to be about 19.7 kilocalories per minute on
each square meterat the equator
above the atmosphere.

A kilocalorie (kcal) is a food Calorie, the kind of Calorie
that we count when we are on diets.

However, all this has been going on at the very top of our
atmosphere. Only about 70% of that energy gets down to sea level.

70% of 9440 kilocalories = 6,600 kilocalories

More Adjustments:

About 4/9 of the solar energy that actually
falls on a plant is energy that the plant can use. (Some of the
radiation does not help with photosynthesis.)

Let's figure out how much energy is
actually useful.

At the equator, a square meter densely
covered with plants is receiving useful radiation of about 4/9
of 6,600 kilocalories per square meter per 24 hour day.

6,600 * 4/9 =2933kilocalories per day

We will round this up to 3000 kilocalories per day for
the sale of simplicity.

Most of this energy is used up by the plant just
being a plant: it has to use energy to do its life processes,
an activity which is called respiration. Under ideal conditions plants might be able to turn
up to about 10% of those 3000 kilocalories into biomass, which is food that
the animals could eat and also stalks and thorns and roots that
may not be digestible, except by detritovores such as bacteria and fungi.

Let's take 10% of the 3000 calories,
remembering that plant tissue may not always be produced at the maximum rate.

3000 kilocalories per day divided by 10 = 300 kilocalories
per square meter per day.

So there are 300 KiloCalories in the new plant tissue
that was added that day. This is called the Net Primary
Productivity per day.

Over a year, how many calories of primary productivity are
produced in our square?

Kilocalories per square meter at 60 Degrees = 1500 kilocalories
per day

These figures are about maximum possible
production during a day which has 12 hours of daylight and12
hours of darkness.

At 60 Degrees Latitude:

As we travel away from the equator, the curvature of the earth
causes the solar energy to be spread out over a larger area.

At 60 degrees North the amount of energy received is about
half that at the equator. There will be more discussion of this
further down on the page.

Additional Variables:

There are spaces between leaves: the energy falling there
is not used.

There are rocks and bare patches on the ground.

Water and nutrients affect growth -- abundant solar energy
is not enough.

Plants grow when it is warm. Brilliant sunlight on a frosty
day is not as effective as brilliant sunlight at the equator!
Animals must eat all year.

Probably the plant yield will usually be lower than the maximum
possible.

These figures are for the energy budget of the earth -sun
system: Check the AU Equivalent in the Star
Tables for your world.

Formulas:

Kcal yield for year = (Calories per
day per square meter) multiplied by (number of days in growing
season).

Latitude

Maximum Kcal for plants per square meter per
24 hour day

Plants use 4/9 of the available
light

Biome

Growing Season in days per
year

Maximum possible light received per square meter
per year

10% turned into plant tissue per
square meter per year

10% turned into animal tissue
by grazing animals per square meter per year

Predator eats animal,
10% becomes predator tissue

0 Equator

6000 (average)

2666

Rain Forest, desert

365 days

973090

97309
K/Cal

97* 5 = 500 K/cal

30 Degrees

5200 (average)

2311

Deciduous
Forest

120-250
days

843515

60 Degrees

4800(midsummer)
3000 (average)
731 (midwinter)

Grasslands

120-200
days

70,000
kcal

70 Degrees

4100(midsummer)
0 (midwinter)

Coniferous
Forest

90-120
days

80 Degrees

3300(midsummer)

0 (midwinter)

Tundra

60-100
days

42,000 -

90 Degrees

At and below a possible
120 days,
earth photo
synthesis is very difficult. This is true in all zones
where plants cannot
get enough light.

Special Cases

The earth's axis is tilted at 23 degrees to the plane of its
rotation around the sun. In the high latitudes near the poles,
winters are dark, and summers have long days. We have heard of
"the midnight sun", which refers to the period when
the sun does not set at the poles. When we think about
the high latitudes, both north and south, we must remember that,
although light is available in abundance, temperatures remain
low. Life processes are chemical processes, which work more quickly
as temperatures rise.